A way to make lighter the graviball is to couple gravitons with light matter fields (of mass much smaller than \(G^{-1/2}\) ). Roughly this will imply to multiply by \(N\)  the unitary loop function \(\ln (-s/\Lambda ^2)\)  in Eq. (), so that the secular equation becomes \(1/(N x_N)+ \ln (-x_N)-i2\pi =0\) , whose approximate solutions scales as \(1/N\) . Then \(s_P=x_N \pi G^{-1}\)  decreases as \(\sim 1/N\) , which makes the graviball lighter and narrower. In some scenarios [1]}, [2]}, [3]} it is expected that \(\Lambda ^2\)  also decreases as \(1/N\)  so that in this case \(x_N\sim x\)  and it does not evolve with \(N\) . However, at the absolute level, once \(x\)  is multiplied by \(\Lambda ^2\) , again \(s_\sigma \sim 1/N\) . Therefore, in theories with large enough number of light degrees of freedom (or with large extra dimensions) the graviball could affect gravitational phenomena at scales that could be tested in colliders (see Ref. [4]} and references thereof).
